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MATHEMATICAL FORECASTING USING THE BOX-JENKINS METHODOLOGY

TECHNICAL BRIEFING

JOSEPH GEORGE CALDWELL, PHD

© 2007 JOSEPH GEORGE CALDWELL.   ALL RIGHTS RESERVED.   POSTED AT INTERNET WEBSITES http://www.foundationwebsite.org AND http://www.foundation.bw .   MAY BE COPIED OR REPOSTED FOR NONCOMMERCIAL USE, WITH ATTRIBUTION.

Note: The document The Box-Jenkins Forecasting Technique, posted at http://www.foundationwebsite.org/BoxJenkins.htm , presents a nontechnical description of the Box-Jenkins methodology.   For a technical description of the Box-Jenkins approach, see the document, TIMES Box-Jenkins Forecasting System, posted at http://www.foundationwebsite.org/TIMESVol1TechnicalBackground.htm .   A computer program that can be used to develop a broad class of Box-Jenkins models is posted at the Foundation website, http://www.foundationwebsite.org (6 February 2009).

BRIEFING ROAD MAP

• 1. MATHEMATICAL FORECASTING CONCEPTS (20-30 MINUTES)

• 2. TECHNICAL INTRODUCTION TO THE BOX-JENKINS METHODOLOGY (20-30)

• 3. FORECASTING ACCURACY COMPARISONS (5-10)

• 4. MODEL BUILDING WITH THE BOX-JENKINS METHODOLOGY (40-60)

• 5. APPLICATION TO ECONOMETRIC AND CONTROL PROBLEMS (10-15)


1. MATHEMATICAL FORECASTING CONCEPTS


MATHEMATICAL FORECASTING METHODOLOGY (“FORECASTER”)

BASED ON A MATHEMATICAL MODEL OF THE PROCESS

TWO APPROACHES

• MODEL FITTING (INTUITIVE, HEURISTIC)

• MODEL BUILDING (THEORETICAL FOUNDATION)


HEURISTIC FORECASTERS

A PARTICULAR MODEL IS FITTED TO DATA

EXAMPLES:

• MOVING AVERAGE
• EXPONENTIAL SMOOTHING
• TRENDS, CURVES, HARMONICS, PATTERNS

GOOD FIT → GOOD FORECAST?

GOOD MODEL → GOOD FORECAST

NEED TO BUILD A GOOD MODEL


MODEL BUILDING

CHOOSE A COMPREHENSIVE CLASS OF MODELS

• IDENTIFICATION
• FITTING
• DIAGNOSTIC CHECKING

REPEAT UNTIL ADEQUATE MODEL CONSTRUCTED


CLASSES OF MODELS (FOR PREDICTION AND CONTROL)

ECONOMETRIC MODELS

• DYNAMIC CAUSAL MODEL (MANY VARIABLES)
•...

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MLA Citation

"Statistics". Anti Essays. 20 Aug. 2018

<https://www.antiessays.com/free-essays/Statistics-84774.html>

APA Citation

Statistics. Anti Essays. Retrieved August 20, 2018, from the World Wide Web: https://www.antiessays.com/free-essays/Statistics-84774.html